<!-- This comment will put IE 6, 7 and 8 in quirks mode -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<title>examples/Supervised/StoppingCriteria.cpp Source File</title>
<script type="text/javaScript" src="search/search.js"></script>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3.0.1/es5/tex-mml-chtml.js"></script>
<script src="../../mlstyle.js"></script>
<link href="../css/besser.css" rel="stylesheet" type="text/css"/>
</head>
<!-- pretty cool: each body gets an id tag which is the basename of the web page  -->
<!--              and allows for page-specific CSS. this is client-side scripted, -->
<!--              so the id will not yet show up in the served source code -->
<script type="text/javascript">
    jQuery(document).ready(function () {
        var url = jQuery(location).attr('href');
        var pname = url.substr(url.lastIndexOf("/")+1, url.lastIndexOf(".")-url.lastIndexOf("/")-1);
        jQuery('#this_url').html('<strong>' + pname + '</strong>');
        jQuery('body').attr('id', pname);
    });
</script>
<body>
    <div id="shark_old">
        <div id="wrap">
            <div id="header">
                <div id="site-name"><a href="../../sphinx_pages/build/html/index.html">Shark machine learning library</a></div>
                <ul id="nav">
                    <li >
                        <a href="../../sphinx_pages/build/html/rest_sources/installation.html">Installation</a>
                    </li>
		    <li >
                        <a href="../../sphinx_pages/build/html/rest_sources/tutorials/tutorials.html">Tutorials</a>
                    </li>
		    <li >
                        <a href="../../sphinx_pages/build/html/rest_sources/benchmark.html">Benchmarks</a>
                    </li>
                    <li class="active">
                        <a href="classes.html">Documentation</a>
                        <ul>
                            <li class="first"></li>
                            <li><a href="../../sphinx_pages/build/html/rest_sources/quickref/quickref.html">Quick references</a></li>
                            <li><a href="classes.html">Class list</a></li>
                            <li class="last"><a href="group__shark__globals.html">Global functions</a></li>
                        </ul>
                    </li>
                </ul>
            </div>
        </div>
    </div>
<div id="doxywrapper">
<!--
    <div id="global_doxytitle">Doxygen<br>Documentation:</div>
-->
    <div id="navrow_wrapper">
<!-- Generated by Doxygen 1.9.8 -->
<div id="nav-path" class="navpath">
  <ul>
<li class="navelem"><a class="el" href="dir_d28a4824dc47e487b107a5db32ef43c4.html">examples</a></li><li class="navelem"><a class="el" href="dir_ca5943d51a26be5f1f9bc4d7d5956bc4.html">Supervised</a></li>  </ul>
</div>
</div><!-- top -->
<div class="header">
  <div class="headertitle"><div class="title">StoppingCriteria.cpp</div></div>
</div><!--header-->
<div class="contents">
<a href="_stopping_criteria_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="preprocessor">#include &lt;<a class="code" href="_csv_8h.html">shark/Data/Csv.h</a>&gt;</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="preprocessor">#include &lt;<a class="code" href="_linear_model_8h.html">shark/Models/LinearModel.h</a>&gt;</span><span class="comment">//single dense layer</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="preprocessor">#include &lt;<a class="code" href="_concatenated_model_8h.html">shark/Models/ConcatenatedModel.h</a>&gt;</span><span class="comment">//for stacking layers to a feed forward neural network</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="preprocessor">#include &lt;<a class="code" href="_rprop_8h.html">shark/Algorithms/GradientDescent/Rprop.h</a>&gt;</span> <span class="comment">//Optimization algorithm</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="preprocessor">#include &lt;<a class="code" href="_cross_entropy_8h.html">shark/ObjectiveFunctions/Loss/CrossEntropy.h</a>&gt;</span> <span class="comment">//Loss used for training</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="preprocessor">#include &lt;<a class="code" href="_zero_one_loss_8h.html">shark/ObjectiveFunctions/Loss/ZeroOneLoss.h</a>&gt;</span> <span class="comment">//The real loss for testing.</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="preprocessor">#include &lt;<a class="code" href="_optimization_trainer_8h.html">shark/Algorithms/Trainers/OptimizationTrainer.h</a>&gt;</span> <span class="comment">// Trainer wrapping iterative optimization</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="preprocessor">#include &lt;<a class="code" href="_max_iterations_8h.html">shark/Algorithms/StoppingCriteria/MaxIterations.h</a>&gt;</span> <span class="comment">//A simple stopping criterion that stops after a fixed number of iterations</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="preprocessor">#include &lt;<a class="code" href="_training_error_8h.html">shark/Algorithms/StoppingCriteria/TrainingError.h</a>&gt;</span> <span class="comment">//Stops when the algorithm seems to converge</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="preprocessor">#include &lt;<a class="code" href="_generalization_quotient_8h.html">shark/Algorithms/StoppingCriteria/GeneralizationQuotient.h</a>&gt;</span> <span class="comment">//Uses the validation error to track the progress</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="preprocessor">#include &lt;<a class="code" href="_validated_stopping_criterion_8h.html">shark/Algorithms/StoppingCriteria/ValidatedStoppingCriterion.h</a>&gt;</span> <span class="comment">//Adds the validation error to the value of the point</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="keyword">using namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>;</div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="keyword">using namespace </span>std;</div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span> </div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment">//this program demonstrates the effect of different stopping criteria on the performance of a neural network.</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="foldopen" id="foldopen00020" data-start="{" data-end="}">
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">   20</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">experiment</a>(</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span>    <a class="code hl_class" href="classshark_1_1_abstract_model.html" title="Base class for all Models.">AbstractModel&lt;RealVector, RealVector&gt;</a>&amp; network, </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span>    <a class="code hl_class" href="classshark_1_1_abstract_stopping_criterion.html" title="Base class for stopping criteria of optimization algorithms.">AbstractStoppingCriterion&lt;T&gt;</a> &amp; stoppingCriterion,</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">ClassificationDataset</a> <span class="keyword">const</span>&amp; trainingset, </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">ClassificationDataset</a> <span class="keyword">const</span>&amp; testset</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span>){</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span>    <a class="code hl_function" href="group__shark__globals.html#gaa2a8823f1241e854ba858d79fd3e37a2" title="Initialize model parameters uniformly at random.">initRandomUniform</a>(network,-0.1,0.1);</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span>    <span class="comment">//The Cross Entropy maximises the activation of the cth output neuron </span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span>    <span class="comment">// compared to all other outputs for a sample with class c.</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span>    <a class="code hl_class" href="classshark_1_1_cross_entropy.html" title="Error measure for classification tasks that can be used as the objective function for training.">CrossEntropy&lt;unsigned int, RealVector&gt;</a> loss;</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span>    <span class="comment">//we use IRpropPlus for network optimization</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span>    <a class="code hl_class" href="classshark_1_1_rprop.html" title="This class offers methods for the usage of the Resilient-Backpropagation-algorithm with/out weight-ba...">Rprop&lt;&gt;</a> optimizer;</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span>    </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span>    <span class="comment">//create an optimization trainer and train the model</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span>    <a class="code hl_class" href="classshark_1_1_optimization_trainer.html" title="Wrapper for training schemes based on (iterative) optimization.">OptimizationTrainer&lt;AbstractModel&lt;RealVector, RealVector&gt;</a>,<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> &gt; trainer(&amp;loss, &amp;optimizer, &amp;stoppingCriterion);</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span>    trainer.<a class="code hl_function" href="classshark_1_1_optimization_trainer.html#ab3cfafba31871515074323c20d501573">train</a>(network, trainingset);</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span>    </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span>    <span class="comment">//evaluate the performance on the test set using the classification loss we choose 0.5 as threshold since Logistic neurons have values between 0 and 1.</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <a class="code hl_class" href="classshark_1_1_zero_one_loss.html" title="0-1-loss for classification.">ZeroOneLoss&lt;unsigned int, RealVector&gt;</a> loss01(0.5);</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span>    <a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;RealVector&gt;</a> predictions = network(testset.<a class="code hl_function" href="group__shark__globals.html#ga6f74e657c7e0c8a32b2456fb328bd653" title="Access to inputs as a separate container.">inputs</a>()); </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>    <span class="keywordflow">return</span> loss01(testset.<a class="code hl_function" href="group__shark__globals.html#ga6328a5aa2570c01a5ac5f25076071663" title="Access to labels as a separate container.">labels</a>(),predictions);</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>}</div>
</div>
<div class="foldopen" id="foldopen00045" data-start="{" data-end="}">
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"><a class="line" href="_stopping_criteria_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">   45</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="_stopping_criteria_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(){</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span>    <span class="comment">//load the diabetes dataset shuffle its entries and split it in training, validation and test set.</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">ClassificationDataset</a> data;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span>    <a class="code hl_function" href="group__shark__globals.html#ga97446d6c453723686391c8896ac27352" title="Import a Dataset from a csv file.">importCSV</a>(data, <span class="stringliteral">&quot;data/diabetes.csv&quot;</span>,<a class="code hl_enumvalue" href="group__shark__globals.html#gga2cd86794253e1e789534ab1c06f4387da17c1671ddb560506fb466c696bd5ce95">LAST_COLUMN</a>, <span class="charliteral">&#39;,&#39;</span>);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    data.<a class="code hl_function" href="group__shark__globals.html#ga96ea65352abe5e2c0787e4154a48972f" title="shuffles all elements in the entire dataset (that is, also across the batches)">shuffle</a>();</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">ClassificationDataset</a> test = <a class="code hl_function" href="group__shark__globals.html#gaa6e44d5e4f847777153927436e61752f" title="Removes the last part of a given dataset and returns a new split containing the removed elements.">splitAtElement</a>(data,<span class="keyword">static_cast&lt;</span>std::size_t<span class="keyword">&gt;</span>(0.75*data.<a class="code hl_function" href="group__shark__globals.html#ga5333445992cd6b14392cd80a1ab5403c" title="Returns the total number of elements.">numberOfElements</a>()));</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>    <a class="code hl_class" href="classshark_1_1_labeled_data.html">ClassificationDataset</a> validation = <a class="code hl_function" href="group__shark__globals.html#gaa6e44d5e4f847777153927436e61752f" title="Removes the last part of a given dataset and returns a new split containing the removed elements.">splitAtElement</a>(data,<span class="keyword">static_cast&lt;</span>std::size_t<span class="keyword">&gt;</span>(0.66*data.<a class="code hl_function" href="group__shark__globals.html#ga5333445992cd6b14392cd80a1ab5403c" title="Returns the total number of elements.">numberOfElements</a>()));</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>    </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>    <a class="code hl_class" href="classshark_1_1_linear_model.html" title="Linear Prediction with optional activation function.">LinearModel&lt;RealVector,LogisticNeuron&gt;</a> layer1(<a class="code hl_function" href="group__shark__globals.html#gae537f0e90beb970397cd7bb9250984e2" title="Return the input dimensionality of a labeled dataset.">inputDimension</a>(data),10); </div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>    <a class="code hl_class" href="classshark_1_1_linear_model.html" title="Linear Prediction with optional activation function.">LinearModel&lt;RealVector&gt;</a> layer2(10,<a class="code hl_function" href="group__shark__globals.html#ga1fee3b5830ae11a78109e8c0265c6569" title="Return the number of classes of a set of class labels with unsigned int label encoding.">numberOfClasses</a>(data));</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>    <a class="code hl_class" href="classshark_1_1_concatenated_model.html" title="ConcatenatedModel concatenates two models such that the output of the first model is input to the sec...">ConcatenatedModel&lt;RealVector&gt;</a> network = layer1 &gt;&gt; layer2;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>    <span class="comment">//simple stopping criterion which allows for n iterations (here n = 10,100,500)</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>    <a class="code hl_class" href="classshark_1_1_max_iterations.html" title="This stopping criterion stops after a fixed number of iterations.">MaxIterations&lt;&gt;</a> maxIterations(10);</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>    <span class="keywordtype">double</span> resultMaxIterations1 = <a class="code hl_function" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">experiment</a>(network, maxIterations,data,test);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>    maxIterations.<a class="code hl_function" href="classshark_1_1_max_iterations.html#a01a37bc2f0b76e3801fed75f699567d6">setMaxIterations</a>(100);</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    <span class="keywordtype">double</span> resultMaxIterations2 = <a class="code hl_function" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">experiment</a>(network, maxIterations,data,test);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>    maxIterations.<a class="code hl_function" href="classshark_1_1_max_iterations.html#a01a37bc2f0b76e3801fed75f699567d6">setMaxIterations</a>(500);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>    <span class="keywordtype">double</span> resultMaxIterations3 = <a class="code hl_function" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">experiment</a>(network, maxIterations,data,test);</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>    </div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>    <a class="code hl_class" href="classshark_1_1_training_error.html" title="This stopping criterion tracks the improvement of the error function of the training error over an in...">TrainingError&lt;&gt;</a> trainingError(10,1.e-5);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>    <span class="keywordtype">double</span> resultTrainingError = <a class="code hl_function" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">experiment</a>(network, trainingError,data,test);</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>    </div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>    <span class="comment">//for the validated stopping criteria we need to define an error function using the validation set</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>    <a class="code hl_class" href="classshark_1_1_cross_entropy.html" title="Error measure for classification tasks that can be used as the objective function for training.">CrossEntropy&lt;unsigned int, RealVector&gt;</a> loss;</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>    <a class="code hl_class" href="classshark_1_1_error_function.html" title="Objective function for supervised learning.">ErrorFunction&lt;&gt;</a> validationFunction(validation,&amp;network,&amp;loss);</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>    <a class="code hl_class" href="classshark_1_1_generalization_quotient.html" title="SStopping criterion monitoring the quotient of generalization loss and training progress.">GeneralizationQuotient&lt;&gt;</a> generalizationQuotient(10,0.1);</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>    <a class="code hl_class" href="classshark_1_1_validated_stopping_criterion.html" title="Given the current Result set of the optimizer, calculates the validation error using a validation fun...">ValidatedStoppingCriterion</a> validatedLoss(&amp;validationFunction,&amp;generalizationQuotient);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>    <span class="keywordtype">double</span> resultGeneralizationQuotient = <a class="code hl_function" href="_stopping_criteria_8cpp.html#a2a736d1bd1f2d88ed3d2e382c7307a59">experiment</a>(network, validatedLoss,data,test);</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>    </div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>    <span class="comment">//print the results</span></div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>    cout &lt;&lt; <span class="stringliteral">&quot;RESULTS: &quot;</span> &lt;&lt; endl;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>    cout &lt;&lt; <span class="stringliteral">&quot;======== \n&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>    cout &lt;&lt; <span class="stringliteral">&quot;10 iterations   : &quot;</span> &lt;&lt; resultMaxIterations1 &lt;&lt; endl;</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>    cout &lt;&lt; <span class="stringliteral">&quot;100 iterations : &quot;</span> &lt;&lt; resultMaxIterations2 &lt;&lt; endl;</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>    cout &lt;&lt; <span class="stringliteral">&quot;500 iterations : &quot;</span> &lt;&lt; resultMaxIterations3 &lt;&lt; endl;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>    cout &lt;&lt; <span class="stringliteral">&quot;training Error : &quot;</span> &lt;&lt; resultTrainingError &lt;&lt; endl;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>    cout &lt;&lt; <span class="stringliteral">&quot;generalization Quotient : &quot;</span> &lt;&lt; resultGeneralizationQuotient &lt;&lt; endl;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>}</div>
</div>
</div><!-- fragment --></div><!-- contents -->
</div>
</body>
</html>
